Attach edge without existing verts
As stated my lemon, there are numerous ways and you need to consider the flow of the topology. Nevertheless, here is the most basic method.


Hover over the edges to the left and press &#9096; CtrlR to loop cut. A purple line will appear during this operation, scrolling the mouse wheel controls the amount of added edge loops. I scrolled once. Confirm with  LMB.
 RMB Select the vertices respectively and make a face with F.